Stirling engines have been in existence for well over a hundred and eighty years, being conceived as a safer alternative to the Steam engine, but they have never attained truly widespread usage. This is generally held to be because of the advent of the Otto internal combustion engine shortly afterward, which generated more power per unit weight, and had easy throttle control, utilising the burning of fossil fuel. Due to environmental concerns and depletion of oil, alternatives to the Otto engine are being sought. The Stirling engine is now resurfacing as a favoured option because of its ability to utilise any external heat source for its power including solar energy, and its potential for high efficiency.
The essential principle of the Stirling engine has been one of creating a cycle in which a gas is consecutively heated at constant pressure, physically expanded, moved to the cooling section, cooled at constant pressure and physically compressed ready to be moved and heated again as the cycle continues. The power stages are the two constant pressure stages, during which heat is either added or taken from the working gas, which causes its volume to increase or decrease, causing a tight fitting power piston to move out or in, in order to maintain constant pressure. Some of the power generated in these two stages is typically stored in a flywheel, the momentum of which is used to physically expand or compress the gas in the other two stages. It also is used to move the gas from the hot end of the engine to the cold end and back, usually by displacing it with a very loose fitting piston, which allows the gas to move around it. The remainder of the power is available for doing work on an external load.
An important feature of the Stirling engine is the regenerator, which sits in the gas flow between the hot end and the cold end. Its function is to take some of the heat from the gas as it is being displaced from the hot end to the cold end, thus reducing the amount of cooling required to attain a low cold end temperature. It then releases this stored heat as the cooled gas is flowing past it again on the way to the hot end, reducing the amount of heat input required to attain a high hot end temperature.
Workings of a Standard Stirling Engine
The following will describe the workings of a conventional Stirling engine. In FIGS. 1A, 1B, 1C and 1D, a section view of a conventional Stirling engine is shown in its four basic stages. In these views, the displacement piston 12 can be taken to be also a simple regenerator, since it sits in the gas flow, and can absorb and re-release heat provided it is made from a thermally conductive material. The hot end 13 of the displacement cylinder 12 is directly above the flame 14, and the cold end is near the heat sink fins 15. A flywheel 16 is shown connected to the two pistons via a crank-shaft 17 and two crank arms, which are shown complete for the sake of clarity even when they occupy a space in front of the section plane. During stage 1, shown in FIG. 1A, the gas is displaced away from the heat sink region 15 cold end, and is being heated in the hot region 13. This causes the gas to expand to a larger than normal volume, expanding past the displacer piston 12 to drive up the power piston 11—which is the only available means of increasing the total internal volume of the gas. This is known as Isothermal expansion, since the temperature and pressure is maintained by an expansion in volume.
During stage 2, shown in FIG. 1B, The energy produced in stage 1 is stored in a flywheel 16, and some of it is used to drive the displacer piston 12 down, now progressively reducing the temperature of the gas to a median temperature, as some of the gas begins to be cooled at the heat sinks 15. If the power piston 11 was not connected to the crank-shaft, it would also decline in response to this, but it can't because flywheel energy is also used to move the power piston against its natural trend to a higher position, which physically expands the gas. This stage is therefore called adiabatic expansion, since it expands due to a means other than heat input.
During stage 3, shown in FIG. 1C, the displacer 12 is now at the hot end 13, forcing most of the gas to the cold end 15, causing temperature and pressure to fall, and therefore the volume to decrease. This sucks the power piston 11 down again. This stage is called isothermal compression.
During stage 4, shown in FIG. 1D, the energy stored in the flywheel 16 is used to move the displacer 12 away from the hot end 13, allowing the cooled air to be heated back to the median temperature. Without the crank shaft 17 and flywheel 16, the power piston 11 would move back up as a result, but it is instead forced further down, causing a net physical compression of the gas by the piston. This stage is called adiabatic compression.
Major Categories of Stirling Engines
Many types and configurations of Stirling engines have been developed apart from the single piston version described above. In broad terms, there are at present, three main classifications. Alpha engines use two tight fitting, crank connected pistons to move gas back and forth with a regenerator in-between. Beta engines (like the one described above) use a single power piston and a displacer piston in essentially the same cylinder, again connected by a crank shaft. Gamma engines have no physical phase connection between the displacer and the power piston, but use springs and dampeners to create a natural frequency in the system, which facilitates an appropriate phase relationship between them.
Others sub classifications include hydraulic, diaphragm and acoustic systems. Generally, Stirling engines rely on a piston/crankshaft arrangement or something similar to deliver the power from the back and forth motion of the piston to the rotary motion of the output drive. Linear alternators have also been employed in some systems to achieve the same basic result: power output from linear reciprocal motion.
Efficiency of a Stirling Engine
The efficiency of a Stirling engine depends upon a number of factors. First of all, the temperature difference between the hot end and the cold end of the engine defines the theoretical limit of efficiency of the engine according to Carnot's equation:
Max Efficiency %=(1−Tc/Th)×100 in which temperatures are in Kelvin, not Celcius, and Tc is the temperature of the cold end of the engine while Th is the temperature in the hot end.
As can be seen from this, as Th increases or Tc decreases, or both, the efficiency approaches 100%. For this reason, extreme temperatures are required for highest efficiency. If Th is around 873 K 600 C and the Tc is roughly ambient 298 K or 25 C, then the maximum efficiency possible would be around 66%. By contrast, the internal combustion engine has a theoretical limit of less than half of this efficiency. It is a fundamental aspect of Carnot's theory that 100% efficiency is impossible as heat flow out of the engine is an essential part of the engine's function. However, it is widely recognised that higher efficiencies are possible in this type of engine than in any other.
From this it can be seen that the theoretical efficiency limit is not the main obstacle to the use of these engines.
Limits to Efficiency
With regard to temperature difference, it is true that the more extreme the temperature used, the greater the insulation required to prevent heat loss—in an exponential, power-4 relationship. Material limitations come into play here, as high temperature metals and insulators are typically exotic and expensive.
A limit to efficiency in the conventional Stirling Engine is the proportion of gas which is never heated or cooled properly because it is not fully displaced, or is trapped somewhere where it cannot be cooled or heated. This is known as dead-space. The proportion of dead space further reduces the efficiency of the engine.
Because the gas is proportionally heated and cooled according to the position of the displacer, when the displacer is anywhere in between its maximum and minimum points, a certain proportion of gas is being cooled while the rest is being heated or vice versa. Because the cycle is rotational in nature, there are only two instants of the cycle in which the gas is all being cooled or all being heated except for the dead space, and therefore only two points at which the forces are not to some extent cancelling each-other out. This leads to reduced efficiency due to a partial cancellation of forces. One way that piston based Stirling engines are being improved in this regard, is by using two mating elliptical gears, which mean that when one is turned at a constant rate, the one it is driving is turning at a variable rate, slowing down at two points in the cycle. This results in the displacer staying longer at both the hot end and the cold end of the cycle, and spending less time in-between. Of course, the ultimate solution would be if there were no need to spend any time in-between, if the air at the hot end was constantly expanding, and the air at the cold end was constantly contracting, with no time lag in-between.
Another related limit to efficiency is the degree to which the gas is heated or cooled in the cycle due to the time allowed. Stirling engines have typically rotary speeds of up to 50,000 rpm, in which case the gas has less than 0.0012 seconds to exchange its heat. This means that there is a minimal exchange of heat in the gas, causing the engine itself to heat up and lose energy to the surroundings without doing work. This reduces the efficiency of the engine.
Another limit to efficiency is air friction as the gas moves to and fro past the displacer. Here we can see that in a Beta displacer type engine, there is a conflict between air friction and dead space efficiency requirements. The more tight fitting the displacer piston, the less dead space, but the more air friction. Air friction increases exponentially with air speed over an object, so this factor becomes more and more important as the rpm of the engine increases.
A major limit to efficiency of existing Stirling engines is the piston/crank arrangement. Careful study of the direction of resultant forces in this arrangement shows that there are transverse component forces acting during rotation, which are pushing the piston arms sideways into the bushings, causing increased friction. There is also a component of force acting directly on the crankshaft rather than tangentially. Only for two brief instants, shown in FIG. 1A and FIG. 1C, is the component of force tangential and acting completely to produce rotational moment. From these two points, the force reduces to zero at stages shown is FIGS. 1B and 1D—where there is no rotational moment in the force whatsoever. It is true that these points generally coincide with points in the cycle when it is primarily energy stored in the flywheel, which carries the two pistons back or forth. However, it remains that even within the two power stroke segments of the cycle—A and C, there are only two brief instants when almost all the force is actually being transmitted into the crank shaft. For most points of the power strokes, there are large components of counter-productive transverse forces. This wastage of forces is great enough to appreciably affect engine efficiency. The effect of these inefficiencies is important in the Stirling Engine, because they affect the power to weight ratio of the engine, and therefore the power to cost ratio, both of which place limitations on the useful applications for the technology.
The fact that these inefficiencies have not yet been overcome is attested by the limited applications in which these engines are currently used. At the time of writing, their main applications are in Submarines, due to their quiet running nature, with a limited application also as on board generators for boats. Much research is underway for engines to be used in power generation from solar, but there are only a few such power plants in operation, and more widespread application of these engine types is not assured with available technology.